CN110222055A - The single-wheel core value maintaining method of multiple edge update under a kind of Dynamic Graph - Google Patents
The single-wheel core value maintaining method of multiple edge update under a kind of Dynamic Graph Download PDFInfo
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Abstract
The invention discloses a kind of single-wheel core value maintaining method of multiple edge update under Dynamic Graph, including insertion point or while when vertex core value maintenance single cycle algorithm and delete point or while when vertex core value safeguard single cycle algorithm.Before updating figure, the node order of a global orderly is safeguarded.Insertion point or while core value maintenance algorithm be added at one time all in single-wheel while, according to order, successively opposite vertexes are begun stepping through later, the influence on the increased vertex of core value is mobile to high order vertex, until the core value on not no vertex changes.Delete point or while core value maintenance algorithm disposably delete all in single-wheel while, and begun stepping through from the vertex for deleting side, by continuous iteration until the core value on all vertex is in stable state.The method of the present invention by single cycle algorithm just complete all vertex core value maintenance, reduce the redundant computation of opposite vertexes in figure ergodic process, reduce core value maintenance time, particularly with for Large Scale Graphs have fabulous scalability and stability.
Description
Technical field
The invention belongs to social network diagram data mining technology fields, more particularly to multiple edge update under a kind of Dynamic Graph
Single-wheel core value maintaining method.
Background technique
Graph data structure can express the relevance between data well.Many realistic problems can be abstracted as diagram data knot
Each example individual is abstracted as the vertex in figure, the relationship between each entity is abstracted as the side between two vertex by structure.
Many big data problems exist all in the form of Large Scale Graphs or network, such as social networks, transportation network figure, infectious disease transmission
The dependency graph of path analysis figure and academic paper.
But flourishing with internet, the scale of figure exponentially increases, and the relationship in figure between vertex is also got over
Come more more complicated, this proposes severe requirement to the parser of Large Scale Graphs.One useful solution is to figure
One subgraph is analyzed, this is because the scale of the subgraph of figure very little compared with entire figure, it is possible to directly answer
Data mining and analysis are carried out to this subgraph with existing nomography.Wherein, core value is a kind of efficient and useful is used to point
The index of close subgraph in figure is analysed, it effectively can be used to measure the compactness of some subgraph in a figure.The K core of one figure
It is a subgraph of figure, each vertex at least K neighbours in this subgraph.For some vertex in figure, if it is possible to
Finding K core includes this vertex, but cannot find a K+1 core includes this vertex, then the core value on this vertex is exactly
K。
But in real life, the vertex or side of figure constantly changed with the time.For example, in social networks
In, with the new account of new user's registration, old user nullifies account, the increase and deletion on vertex in corresponding diagram, phase between user
Mutual plusing good friend or the increase and deletion for deleting side in good friend's corresponding diagram.In such dynamic network, with the increase on point or side
And deletion, the core value on each vertex is also changing in figure.In Dynamic Graph, updated with increase and the deletion on point or side
The problem of each vertex core value referred to as core value maintenance issues.The difficult point of core value maintenance issues is the variation with figure, needs
The core value for distinguishing each vertex in figure has changed the core value on how many and which vertex and has really been changed.
Existing core value maintenance algorithm finds the knot of side composition by the method for successive ignition in each iteration
Structure ensures that the core value on all vertex can only at most increase by 1.But this algorithm needs to require in each iteration finding
One available structure, this will spend many unnecessary times.Particularly, the time overhead for finding the cost of this structure accounts for often
The ratio of secondary iteration total time is higher, shares equally, and will be a no small time overhead.
Summary of the invention
The present invention provides a kind of single-wheel core value maintaining method of multiple edge update under Dynamic Graph, to solve the existing dynamic kernel of graph
Technical problem in value maintenance process because needing the iteration for carrying out multiple algorithm to cause time overhead excessively high.
The technical scheme to solve the above technical problems is that the single-wheel core value of multiple edge update is tieed up under a kind of Dynamic Graph
Maintaining method is tieed up when the insertion point under the Dynamic Graph of social networks or side using vertex core value when insertion point under Dynamic Graph or side
Submethod is protected, vertex core value maintenance submethod includes:
S1, the candidate degree on each vertex, core value and stop degree in current Dynamic Graph are determined, and each vertex is sorted out, formed more
A k-order set Ok, k is the OkIn the current core value in each vertex；
S2, based on all points to be inserted into or side, update the candidate degree on each vertex；
S3, the sequence according to k from small to large determine an Ok, it is based on the OkIn a vertex v candidate degree and stop degree, sentence
Whether the vertex v of breaking is that core value increases point；
S4, if so, updating the OkMiddle order comes the stop degree on neighbours vertex thereafter, and to the OkMiddle order follows top closely
Next vertex of point v executes S3；Otherwise, the stop degree based on the vertex v selects next vertex to execute S3 or updates the vertex
The candidate degree of v and stops degree simultaneously select next vertex execution S3 after transmitting the not increased influence of vertex v core value；
Wherein, if the OkIn all vertex traversed, then by it is all be not core value increase point vertex add in order
To next Ok, and to updated next OkS3 is executed, until having traversed all Ok, obtain the core value update on each vertex
Value completes the maintenance of core value.
The beneficial effects of the present invention are: the present invention is that one kind only passes through single-wheel in the case that multiple summits update in Dynamic Graph
Algorithm just completes the quickly and effectively vertex core value maintaining method that all vertex core values update.The inventive method is updating figure
Before, it first safeguards the node order of a global orderly, all sides is added at one time in single-wheel, later according to order successively to top
Point is begun stepping through, and the influence on the increased vertex of core value is mobile to high order vertex, until the core value on not no vertex changes.
The method of the present invention just completes the core value maintenance on all vertex by single cycle algorithm, reduces the superfluous of opposite vertexes in figure ergodic process
Remaining calculating, reduce core value maintenance time, particularly with for Large Scale Graphs have fabulous scalability and stability.
On the basis of above-mentioned technical proposal, the present invention can also be improved as follows.
Further, the candidate degree for updating each vertex, specifically:
It is corresponding in O to each institute's edgedkThe candidate Du Jia 1 on the middle preceding vertex of order, completes the candidate on each vertex
Degree updates.
It is further, described to judge whether the vertex v is that core value increases point, specifically:
Judge the OkWhether the candidate degree of middle vertex v and the adduction of stop degree are greater than k, if so, judging that vertex v is core value
Increase point, otherwise, judges that vertex v is that non-core value increases point.
Further, the stop degree on each vertex is preset as zero in the current Dynamic Graph；
Then S4 includes:
S4.1, if so, in the OkThe stop degree that middle order comes neighbours vertex thereafter adds one, and to the OkMiddle order
The next vertex for following vertex v closely executes S3；If it is not, executing S4.2；
Whether S4.2, the stop degree for judging the vertex v are zero, if so, coming the candidate on each vertex thereafter according to order
Degree and stop degree, selection execute S3 to next vertex；If it is not, executing S4.3；
S4.3, the adduction that the candidate degree of vertex v is updated to current candidate degree and stop degree, by the stop degree of vertex v
It is updated to zero, transmitting the vertex v core value increased cannot influence, and comes the candidate degree on each vertex thereafter according to order and stop
Office Copy selects next vertex to execute S3.
Further beneficial effect of the invention is: judging that the stop degree on vertex is equal to 0 or not equal to 0, is that its is right for exclusion
Whether the neighbours vertex of front causes core value to influence, and when being equal to 0, illustrating front neighbours vertex is not core value enhancer,
So not having to consider the vertex, which will not be the changed vertex of core value, improve calculating speed.
Further, in the S4.2, the candidate degree and stop degree that each vertex thereafter is come according to order, under selection
One vertex executes S3, specifically:
Judge the OkIn come first candidate degree after vertex v with the presence or absence of order and be greater than the top of k or stop degree greater than 0
Point u, if so, vertex u is determined as next vertex and executes S3, if it is not, the then OkIn all vertex traversed.
Further beneficial effect of the invention is: for not being the increased vertex v of core value, then coming top thereafter to order
Point is judged, the candidate degree and stop degree on subsequent vertex can be first passed through, and tentatively to judge whether to may be that core value increases
Vertex, then carry out the maintenance of subsequent core value again, improve calculating speed, reduce time overhead.
Further, in the S4.3, described transmitting not increased influence of vertex v core value, specifically:
(a) the candidate degree that each of the vertex v belongs to the neighbours vertex m that core value increases point is subtracted 1, if neighbours vertex m
Candidate degree and the sum of stop degree be less than k, then the core value for deleting neighbours vertex m increases the label of point, and updates neighbours top
The candidate degree of point m is the adduction of current candidate degree and stop degree, stop degree is zero；
(b) to each neighbours vertex w of neighbours vertex m, if neighbours vertex w is in OkIn come the vertex v after, then
The stop degree of neighbours vertex w is subtracted 1, otherwise, opposite vertexes w repeats the transmitting operation such as vertex m in step (a).
The present invention also provides a kind of single-wheel core value maintaining methods of multiple edge update under Dynamic Graph, when the dynamic in social networks
When the lower deletion point of figure or side, submethod is safeguarded using vertex core value when deleting point or side under Dynamic Graph, which safeguards son
Method includes:
S1, the goodness number and core value for determining each vertex in current Dynamic Graph；
S2, based on all points to be deleted or side, update the goodness number on each vertex；
S3, the vertex that its each goodness number is less than its core value is determined as to core value reduction point；
S4, the core value that point is reduced based on each core value determine that the core value of other omissions reduces point from all vertex；
S5, the core value and goodness number for updating each core value reduction point, and S3 is repeated, until there is no core values to reduce
Point obtains the core value updated value on each vertex, completes the maintenance of core value.
The beneficial effects of the present invention are: the present invention is that one kind only passes through single-wheel in the case that multiple summits update in Dynamic Graph
Algorithm just completes the quickly and effectively vertex core value maintaining method that all vertex core values update.The inventive method is updating figure
Before, first safeguard the node order of a global orderly, the vertex core value maintenance algorithm for deleting point set or side collection is primary in single-wheel
Property delete all sides, and begun stepping through from the vertex for deleting side, by continuous iteration until the core value on all vertex is in
Stable state.The method of the present invention just completes the core value maintenance on all vertex by single cycle algorithm, reduces in figure ergodic process
The redundant computation of opposite vertexes reduces the time of core value maintenance, particularly with for Large Scale Graphs with fabulous scalability and
Stability.
Further, the S4 includes:
Determine that each core value reduces its core value of each of point neighbours vertex equal with the core value of core value reduction point, and will be every
The goodness number on a neighbours vertex subtracts 1, if the goodness number on the neighbours vertex is less than its core value, which is determined as core value and is subtracted
Few point.
Further, the S5 includes
The core value that each core value reduces point is subtracted 1 and updates goodness number, if the core value reduces point and repeats S3, otherwise,
Then deleting the vertex is the label that core value reduces point, until there is no core values to reduce point, obtains the core value updated value on each vertex,
Complete the maintenance of core value.
The present invention also provides a kind of storage medium, instruction is stored in the storage medium, when computer reads the finger
When enabling, make the computer execute when such as insertion point under above-mentioned any Dynamic Graph or side vertex core value maintenance submethod and/or
As vertex core value safeguards submethod when deleting point or side under above-mentioned any Dynamic Graph.
Detailed description of the invention
Fig. 1 is insertion point or vertex core value safeguards submethod when side under a kind of Dynamic Graph provided by one embodiment of the present invention
Flow diagram；
The flow chart that vertex core value updates when Fig. 2 is insertion side provided by one embodiment of the present invention；
Fig. 3 be it is provided by one embodiment of the present invention insertion while when insertion while before original image schematic diagram；
Fig. 4 be the corresponding insertion of Fig. 3 while when by while be added to the new diagram intention that original image obtains；
Fig. 5 is that vertex core value safeguards submethod when deleting point or side under a kind of Dynamic Graph provided by one embodiment of the present invention
Flow diagram；
The flow chart that vertex core value updates when Fig. 6 is deletion side provided by one embodiment of the present invention；
Fig. 7 be it is provided by one embodiment of the present invention delete while when delete while before original image schematic diagram；
Fig. 8 be Fig. 7 it is corresponding delete while when by while from original image delete after obtain new diagram intention.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below
Not constituting a conflict with each other can be combined with each other.
Embodiment one
The single-wheel core value maintaining method of multiple edge update under a kind of Dynamic Graph, when the insertion point under the Dynamic Graph of social networks or
Bian Shi safeguards submethod 100 using vertex core value when insertion point under Dynamic Graph or side, as shown in Figure 1, vertex core value maintenance
Method includes:
Step 110 determines the candidate degree on each vertex, core value and stop degree in current Dynamic Graph, and each vertex is sorted out, shape
At multiple k-order set Ok, k is the OkIn the current core value in each vertex；
Step 120, based on all points to be inserted into or side, update the candidate degree on each vertex；
Step 130, the sequence according to k from small to large determine an Ok, it is based on the OkIn a vertex v candidate degree and stop
Degree judges whether the vertex v is that core value increases point；
Step 140, if so, updating the OkMiddle order comes the stop degree on neighbours vertex thereafter, and to the OkMiddle order is tight
Step 130 is executed with next vertex of vertex v；Otherwise, the stop degree based on the vertex v selects next vertex to execute step
It 130 or updates the candidate degree of the vertex v and stop degree and selects next vertex after transmitting the not increased influence of vertex v core value
Execute step 130；Wherein, if the OkIn all vertex traversed, then by it is all be not core value increase point vertex in order
It is added to next Ok, and to updated next OkStep 130 is executed, until having traversed all Ok, obtains each vertex
Core value updated value completes the maintenance of core value.
It should be noted that the core value k's on each vertex is determined as: needs can look for a subgraph, in this subgraph, often
The degree on a vertex is more than or equal to k, and k is the largest, then the k value is the core value on the vertex.K-order construction method are as follows: a, look for
The smallest vertex set of figure moderate, from one vertex of random erasure in the set, b, later, according to the deletion sequence of step a,
Construct this k-order..The candidate degree on one vertex determines method are as follows: the neighbours after the vertex are come in k-order
The number on vertex, wherein all neighbours vertex being mentioned herein are for full figure.Stop degree is defined as in k-
The front is come in order and is located at belongs to neighbours' number of vertices that core value increases point.It is every in current Dynamic Graph in step 110
The candidate degree on a vertex is the updated value after last time core value maintenance algorithm is finished.
The present embodiment only passes through an algorithm iteration, and whole change is reduced by the way that whole sides is added in algorithm iteration
Generation number, in addition, the number on the vertex needed to be traversed for is reduced in an iterative process, the top that will be needed to be traversed in entire maintenance process
Point number greatly reduces, so the time required for entire maintenance process is significantly reduced compared with existing algorithm, has
Lower time complexity.Secondly, the scalability of the present embodiment is strong, two aspects are embodied in, on the one hand for advising with index
For the figure that mould increases, it is added or is deleted point or the side of same size, can still be handled with time that linear scale increases
The update of core value.On the other hand, for specific Large Scale Graphs, it is added or deletes the point increased with index scale or side
When, the time of maintenance k core is also linearly to increase.So with the rule of original image scale and the point or side that are dynamically added or delete
The growth of mould, the present invention can be handled efficiently, have very strong scalability.In addition, specific big for some
Scale figure safeguards the time of core value all very every time in continuous addition during/addition point or when deleting/deletion point
Stablize, be not in larger fluctuation, which can significantly reduce the whole delay of system, improve the stability of system.
The present embodiment is that one kind only just completes all tops by single cycle algorithm in the case that multiple summits update in Dynamic Graph
The quickly and effectively vertex core value maintaining method that point core value updates.The inventive method first safeguards an overall situation before updating figure
Orderly node order is added at one time all sides in single-wheel, and according to order, successively opposite vertexes are begun stepping through later, by core value
The influence on increased vertex is mobile to high order vertex, until the core value on not no vertex changes.The method of the present invention passes through list
Wheel algorithm just completes the core value maintenance on all vertex, reduces the redundant computation of opposite vertexes in figure ergodic process, reduces core
Be worth maintenance time, particularly with for Large Scale Graphs have fabulous scalability and stability.
Preferably, the candidate degree on each vertex is updated, specifically:
It is corresponding in O to each institute's edgedkThe candidate Du Jia 1 on the middle preceding vertex of order, completes the candidate on each vertex
Degree updates.
Preferably, judge whether the vertex v is that core value increases point, specifically:
Judge the OkWhether the candidate degree of middle vertex v and the adduction of stop degree are greater than k, if so, judging that vertex v is core value
Increase point, otherwise, judges that vertex v is that non-core value increases point.
Due to vertex core value are as follows: the neighbours vertex that at least k core value is more than or equal to k at most has k core value to be more than or equal to
The neighbours vertex of k+1.Definition and aforementioned maintenance process based on candidate degree and stop degree, if the candidate degree of the point and stop degree
Adduction be greater than the vertex core value, then illustrate that the core value on the vertex can increase 1, then it is assumed that the vertex be possible core value variation
Point.
Preferably, the stop degree on each vertex is set as zero in current Dynamic Graph, then step 140 includes:
Step 141, if so, in the OkThe stop degree that middle order comes neighbours vertex thereafter adds one, and to the OkIn time
Next vertex that sequence follows vertex v closely executes S3；If it is not, executing step 142；
Whether step 142, the stop degree for judging the vertex v are zero, if so, coming the time on each vertex thereafter according to order
Degree of choosing and stop degree select next vertex to execute step 130；If it is not, executing step 143；
Step 143, the adduction that the candidate degree of vertex v is updated to current candidate degree and stop degree, by the stop of vertex v
Degree be updated to zero, transmitting the vertex v core value increased cannot influence, and according to order come each vertex thereafter candidate degree and
Stop degree selects next vertex to execute step 130.
It should be noted that the stop degree initial value on a vertex is 0, the judgement whether changed by a core value
Later, 1 is added to the stop degree on each neighbours vertex in k-order thereafter.
Judge that the stop degree on vertex is equal to 0 still not equal to 0, is to exclude whether it causes core to the neighbours vertex of front
Value influences, and when being equal to 0, illustrating front neighbours vertex is not core value enhancer, so not having to consider the vertex, the vertex is not
It can be the changed vertex of core value, improve calculating speed.
Preferably, in step 142, the candidate degree and stop degree on each vertex thereafter are come according to order, is selected next
Vertex executes step 130, specifically:
Judge the OkIn come first candidate degree after vertex v with the presence or absence of order and be greater than the top of k or stop degree greater than 0
Point u, if so, vertex u is determined as next vertex and executes step 130, if it is not, the then OkIn all vertex traversed.
It should be noted that the core value on all vertex is equal in a k-order and is k, though candidate degree and core value
So it is not directly dependent upon, but candidate's degree is for judging the possible increased condition of the core value of current vertex, candidate degree is to indicate
Come behind current vertex (be not limited to current k-order, be for all k-order, such as it is all in 2-order
The part neighbours vertex that vertex comes the current vertex in 1-order after all vertex, in 1-order may be
In 2-order, the neighbours vertex in 2-order can also be contributed the candidate degree of the current vertex) neighbours vertex number.
For not being the increased vertex v of core value, then to the OkMiddle order comes vertex thereafter and is judged, can first lead to
The candidate degree and stop degree for crossing subsequent vertex, tentatively judge whether to may be the increased vertex of core value, then carry out subsequent
Core value maintenance, improve calculating speed, reduce time overhead.
Preferably, in step 143, the not increased influence of vertex v core value is transmitted, specifically:
(a) the candidate degree that each of the vertex v belongs to the neighbours vertex m that core value increases point is subtracted 1, if neighbours vertex m
Candidate degree and the sum of stop degree be less than k, then the core value for deleting neighbours vertex m increases the label of point, and updates neighbours top
The candidate degree of point m is the adduction of current candidate degree and stop degree, stop degree is zero；
(b) to each neighbours vertex w of neighbours vertex m, if neighbours vertex w is in OkIn come the vertex v after, then
The stop degree of neighbours vertex w is subtracted 1, otherwise, opposite vertexes w repeats the transmitting operation such as vertex m in step (a).
It should be noted that candidate's degree is to count the neighbours' number of vertices come thereafter.Category was judged before the vertex
In the stop degree that the increased neighbours' number of vertices of core value is the vertex, to these neighbours vertex are put into Ok+1In, so putting
After setting, these neighbours vertex are located at behind the vertex, so using the candidate Du Jia stop degree on the vertex as the vertex
New candidate degree, for updating next time.
For example, insertion point or k core safeguards submethod when side under Dynamic Graph, as shown in Figure 2, comprising the following steps:
(11) all vertex are classified as different k-order according to different core values, are denoted as O by initial timeK.Each
Safeguard two degree: candidate degree (CD) and stop degree (RD) in vertex:
CD (v)=| { u ∈ neighbor (v): v≤u } |,
RD (v)=| u ∈ neighbor (v): u≤v ∧ core (u)
=core (v) ∧ u is a potential candidate |
Wherein, vertex u is the neighbours vertex of vertex v, and core (u) indicates that the nucleus number of vertex u, core (v) indicate vertex v
Nucleus number.Initial time, the candidate degree CD on each vertex are equal to the candidate degree being calculated when last update point or side, Mei Geding
The stop degree of point is set to 0.
(12) all sides to be inserted into are traversed<u,v>, by side<u,v>original image is added, and updates the candidate degree of respective vertices,
Specifically, the candidate degree of vertex u is increased by 1 if the nucleus number of vertex u is less than the nucleus number of vertex v；Else if the core of vertex u
Number is greater than the nucleus number of vertex v, and the candidate degree of vertex v is increased by 1；Otherwise the nucleus number of vertex u is equal to the nucleus number of vertex v, at this time such as
The candidate degree of vertex u is then increased by 1 before the order of vertex v by the order of fruit vertex u, otherwise increases the candidate degree of vertex v
1。
(13) each O is traversedk, by set of candidates VCWith new OkQueue Ok' it is initialized as sky.It is traversed according to order
To OkIn some vertex viWhen, if CD (vi) and RD (vi) the sum of be greater than k, step (14) are jumped to, else if RD (vi)
Equal to 0, step (15) are jumped to, otherwise jump to step (16).All O are traversedkWhole flow process terminates afterwards；
(14) by viFrom OkMiddle removal is simultaneously added in set of candidates.V is greater than for orderiEach nucleus number be equal to k
(in OkIn) neighbours vertex, the stop degree of the neighbours is increased by 1.Order, which is continued with, then according to step (13) follows v closelyi's
Next vertex；
(15) O is foundkMiddle order is in viFirst later meets candidate's degree CD and is greater than the top that k or stop degree RD is greater than 0
Point vj.If the v for meeting this condition cannot be foundj, step (17) are jumped to, otherwise by vi,…,vj-1From OkMiddle removal is simultaneously pressed
Sequence is appended to Ok' in go (another null set).Then step (13) is jumped to from vjStart to continue with OkMiddle vertex；
(16) by viFrom OkMiddle removal is simultaneously appended to Ok', update viCandidate degree CD be current candidate degree CD and stop degree RD
The sum of, stop degree is set as 0, transmits viNucleus number increased cannot influence, and then branching to step (13), to continue with order tight
With viNext vertex.Specifically:
(161) an initial empty queue, for vertex viEach neighbour in set of candidates, by the neighbours
The candidate degree CD on vertex subtracts 1, if the sum of the candidate degree of the neighbours and stop degree are less than k, which is added to team
In column；
(162) if queue is sky, terminate process；Otherwise a vertex u is removed from queue, updates the candidate on the vertex
Degree is the sum of candidate's degree and stop degree, and stop degree is set as 0, which is removed from set of candidates and is appended to Ok′；
(163) for the vertex u being removed in step (162), the neighbours w of k is equal to for each nucleus number of vertex u, such as
Fruit vertex viOrder before the w of vertex, then jump to step (164), else if the order of vertex u before the w of vertex simultaneously
And vertex w then jumps to step (165) in set of candidates, else if vertex w is before the u of vertex and vertex w is in candidate
In person's set, step (166) are jumped to；
(164) the stop degree of vertex w is reduced 1；
(165) the stop degree of vertex w is reduced 1, if the sum of the candidate degree of vertex w and stop degree less than or equal to K and
Vertex w was not added in queue, then vertex w was added in queue；
(166) the candidate degree of vertex w is reduced 1, if the sum of the candidate degree of vertex w and stop degree less than or equal to K and
Vertex w was not added in queue, then vertex w was added in queue.
(17) at this point for set of candidates VCIn each vertex, degree of being stopped is set as 0, and nucleus number increases by 1, and presses
According to vertex in OkIn sequence be successively added to Ok+1Before, Ok' become new Ok.Then step (13) is jumped to continue with
Ok+1。
Further, specific example is as shown in Figure 3 and Figure 4, and when being inserted into side, core value maintaining method is such as under efficient Dynamic Graph
Under:
1) share 9 vertex in Fig. 3, number 0-8, the core value on each vertex of initial time be 1,1,1,2,2,2,2,
2,2}.K-order is established for all nodes, wherein O1={ 2,1,0 }, O2={ 5,4,3,6,8,7 }.Calculate stopping for each vertex
Office Copy is set to 0, according to formula calculate each vertex candidate degree be CD (0)=1, CD (1)=1, CD (2)=1, CD (3)=
1, CD (4)=2, CD (5)=2, CD (6)=2, CD (7)=0, CD (8)=1.
2) 3 chain-dotted lines are the sides being newly added in Fig. 4.Original image is added in this 3 sides being newly added, and updates respective vertices
Candidate degree.Addition side<2,3>, CD (2)=2, addition side<5,7>, CD (5)=3, addition side<6,4>, CD (4)=3.
3) O is traversed1In vertex, by set of candidates VCWith new OkQueue Ok' it is initialized as sky.Vertex 2 is first accessed,
Because CD (2)+RD (2)=2 > 1, is added to set of candidates for vertex 2, the core value on vertex 2 is equal to 1 and order is greater than vertex
The stop degree of 2 neighbours adds 1, i.e. RD (1)=1.Next access vertex 1 adds vertex 1 because of CD (1)+RD (1)=2 > 1
Enter to set of candidates, the core value on vertex 1 is equal to 1 and order is greater than the stop degree of neighbours on vertex 1 and adds 1, i.e. RD (0)=1.
Next access vertex 0, because CD (0)+RD (0)=2 > 1, is added to set of candidates for vertex 0, by the core value etc. on vertex 0
In 1 and order be greater than the stop degree of neighbours on vertex 0 and add 1, meet condition without neighbours at this time.Vertex 2,1,0 is stopped at this time
Office Copy set 0 and core value add 1, and be added to O2In.
4) O is traversed2In vertex, by set of candidates VCWith new OkQueue Ok' it is initialized as sky.Vertex 2 is first accessed,
CD (2)+RD (2)=2, and CD (2) is not equal to 0, finds the vertex that first candidate's degree is greater than 0 greater than k or stop degree backward,
That is vertex 5.By vertex 2,1,0 from O2Middle removal is appended to O2' in.Because CD (5)+RD (5)=3 > 2, is added to time for vertex 5
In the person's of choosing set, the core value on vertex 5 is equal to 2 and order is greater than the stop degree of neighbours on vertex 5 and adds 1, i.e. RD (4)=1, RD
(6)=1, RD (7)=1.Next access vertex 4, because CD (4)+RD (4)=4 > 2, is added to set of candidates for vertex 4
In, by the core value on vertex 4 be equal to 2 and order be greater than vertex 4 stop degree add 1, i.e. RD (3)=1, RD (6)=2, RD (7)=2.
Next access vertex 3, because of CD (3)+RD (3)=2, and CD (3) is not equal to 0, find backward first candidate degree be greater than k or
Person's stop degree is greater than 0 vertex, i.e. vertex 6.Next access vertex 6, because CD (6)+RD (6)=4 > 2, vertex 6 is added
Into set of candidates, the core value on vertex 6 is equal to 2 and order is greater than the stop degree of neighbours on vertex 6 and adds 1, i.e. RD (8)=1,
RD (7)=3.Next access vertex 8, because CD (8)+RD (8)=2, and CD (8) is not equal to 0, finds first candidate backward
Degree is greater than the vertex of k or stop degree greater than 0, i.e. vertex 7.It next processing vertex 7 will because of CD (7)+RD (7)=4 > 2
Vertex 7 is added in set of candidates, and the core value on vertex 7 is equal to 2 and order is greater than the stop degree of neighbours on vertex 7 and adds 1, this
When there is no neighbours to meet condition.At this time by the stop degree on vertex 5,4,3,7 set 0 and core value add 1, and be added to O3In.
5) O is next traversed3, access vertex 5, CD (5)+RD (5)=3 first, and CD (5) is not equal to 0, finds the backward
One candidate's degree is greater than the vertex of k or stop degree greater than 0, can not find the vertex of the condition of satisfaction at this time, terminates traversal O3.This
When, all OkAll traversal finishes, and algorithm terminates.The core value on each vertex is { 2,2,2,2,3,3,3,3,2 } after update.
Embodiment two
The single-wheel core value maintaining method of multiple edge update under a kind of Dynamic Graph, when deleted under the Dynamic Graph of social networks point or
Bian Shi safeguards submethod 200 using vertex core value when deleting point or side under Dynamic Graph, as shown in figure 5, vertex core value maintenance
Method includes:
Step 210, the goodness number and core value for determining each vertex in current Dynamic Graph；
Step 220, based on all points to be deleted or side, update the goodness number on each vertex；
The vertex that its each goodness number is less than its core value is determined as core value reduction point by step 230；
Step 240, the core value that point is reduced based on each core value determine that the core value of other omissions is reduced from all vertex
Point；
Step 250, the core value and goodness number for updating each core value reduction point, and step 230 is repeated, until being not present
Core value reduces point, obtains the core value updated value on each vertex, completes the maintenance of core value.
It should be noted that the goodness number on a vertex is on the neighbours vertex that core value is more than or equal to the vertex core value
Number.
The present embodiment is that one kind only just completes all tops by single cycle algorithm in the case that multiple summits update in Dynamic Graph
The quickly and effectively vertex core value maintaining method that point core value updates.The inventive method first safeguards an overall situation before updating figure
Orderly node order, deletes point set or when the vertex core value maintenance algorithm of collection disposably deletes all in single-wheel, and from
The vertex for deleting side is begun stepping through, by continuous iteration until the core value on all vertex is in stable state.Side of the present invention
Method just completes the core value maintenance on all vertex by single cycle algorithm, reduces the redundant computation of opposite vertexes in figure ergodic process,
The time for reducing the maintenance of core value has fabulous scalability and stability especially for Large Scale Graphs.
Preferably, step 240 includes:
Determine that each core value reduces its core value of each of point neighbours vertex equal with the core value of core value reduction point, and will be every
The goodness number on a neighbours vertex subtracts 1, if the goodness number on the neighbours vertex is less than its core value, which is determined as core value and is subtracted
Few point.
Preferably, step 250 includes
The core value that each core value reduces point is subtracted 1 and updates goodness number, if the core value reduces point and repeats step 230,
Otherwise, then deleting the vertex is the label that core value reduces point, until there is no core values to reduce point, obtains the core value on each vertex more
New value completes the maintenance of core value.
Goodness number MCD is expressed as follows:
MCD (v)=| { u ∈ neighbor (v): core (u) >=core (v) } |.
Specific example is as Figure 6-Figure 8, and when deleting side, core value maintaining method is as shown in Figure 6 such as under efficient Dynamic Graph
Under:
1) Fig. 7 is the figure before deleting side.6 nodes, number 0-5, the core on each vertex of initial time are shared in figure
Value is { 2,2,2,2,2,2 }.The cd value (cd [u]=MCD (u)) on each vertex is set as 0, and the goodness number on each vertex is respectively
{4,2,4,3,2,3}.Fig. 8 be delete side collection<0,5>,<0,2>,<2,3>,<4,5>} after figure.
2) all sides to be deleted are traversed, the goodness number on each vertex is updated.Deletion side<0,5>, MCD (0)=3, MCD
(5)=2.Deletion side<0,2>, MCD (0)=2, MCD (2)=3.Deletion side<2,3>, MCD (3)=2, MCD (2)=2.Delete side
<4,5>, MCD (4)=1, MCD (5)=1.The goodness number on last each vertex is respectively { 2,2,2,2,1,1 }.
3) in 2), the goodness number on discovery vertex 4 and vertex 5 is less than the core value on vertex, and vertex 4 and 5 is added to set
SuIn.Su={ 4,5 }.
4) 0 is set by the access identities position on vertex in figure and rejecting marker.
5) for current collection SuIn each vertex, removed [4]=visited [4]=1, cd [4]=MCD (4)
=1, removed [5]=visited [5]=1, cd [5]=MCD (5)=1.Empty stack Stk is initialized, vertex 4 and 5 is successively pressed
Enter to stack Stk.
6) vertex 5 is hit by a bullet out from stack, the cd value on the neighbours vertex 3 on vertex 5 is reduced 1, it is small to be equal to 1 by cd [3] at this time
Work as pronucleus value 2 in it, vertex 3 is pressed into stack and removed [3]=1 are set.
7) vertex 3 is hit by a bullet out from stack, the cd value of the neighbours 0 on vertex 3 is reduced 1, cd [0] is equal to 1 and is less than it at this time
When pronucleus value 2, vertex 0 is pressed into stack and removed [0]=1 is set.
8) vertex 0 is hit by a bullet out from stack, the cd value of the neighbours 1 on vertex 0 is reduced 1, cd [1] is equal to 1 and is less than it at this time
When pronucleus value 2, vertex 1 is pressed into stack and removed [1]=1 is set.
9) vertex 1 is hit by a bullet out from stack, the cd value of the neighbours 2 on vertex 1 is reduced 1, cd [2] is equal to 1 and is less than it at this time
When pronucleus value 2, vertex 2 is pressed into stack and removed [2]=1 are set.
10) vertex 2 is hit by a bullet out from stack, there is no the neighbours that removed is false on vertex 2 at this time, without new node
It is pressed into stack.
11) vertex 4 is hit by a bullet out from stack, there is no the neighbours that removed is false on vertex 4 at this time, without new node
It is pressed into stack.
12) stack is sky at this time, the core value for the node that all removed are true is reduced 1, at this time the core value of each node
Respectively { 1,1,1,1,1,1 }.
13) the goodness number on each vertex is recalculated, there is no the goodness numbers of node to be less than its core value 1 at this time, so Su
For sky, algorithm terminates.The core value of final each node is { 1,1,1,1,1,1 }.
Embodiment three
A kind of storage medium is stored with instruction in storage medium, when computer reads described instruction, makes the computer
Vertex core value maintenance submethod and/or such as embodiment when executing under any Dynamic Graph as described in embodiment one insertion point or side
Vertex core value safeguards submethod when deleting point or side under any Dynamic Graph described in two.
Related art scheme is with embodiment one and embodiment two, and details are not described herein.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should all include
Within protection scope of the present invention.
Claims (10)
1. the single-wheel core value maintaining method of multiple edge update under a kind of Dynamic Graph, which is characterized in that when the Dynamic Graph in social networks
When lower insertion point or side, submethod is safeguarded using vertex core value when insertion point under Dynamic Graph or side, which safeguards son side
Method includes:
S1, the candidate degree on each vertex, core value and stop degree in current Dynamic Graph are determined, and each vertex is sorted out, form multiple k-
Order set Ok, k is the OkIn the current core value in each vertex；
S2, based on all points to be inserted into or side, update the candidate degree on each vertex；
S3, the sequence according to k from small to large determine an Ok, it is based on the OkIn a vertex v candidate degree and stops degree, judge this
Whether vertex v is that core value increases point；
S4, if so, updating the OkMiddle order comes the stop degree on neighbours vertex thereafter, and to the OkMiddle order follows vertex v closely
Next vertex executes S3；Otherwise, the stop degree based on the vertex v selects next vertex to execute S3 or updates the time of the vertex v
Degree of choosing and stops degree simultaneously select next vertex execution S3 after transmitting the not increased influence of vertex v core value；
Wherein, if the OkIn all vertex traversed, then by it is all be not core value increase point vertex be added in order it is next
A Ok, and to updated next OkS3 is executed, until having traversed all Ok, the core value updated value on each vertex is obtained, is completed
The maintenance of core value.
2. the single-wheel core value maintaining method of multiple edge update under a kind of Dynamic Graph according to claim 1, which is characterized in that institute
The candidate degree for updating each vertex is stated, specifically:
It is corresponding in O to each institute's edgedkThe candidate Du Jia 1 on the middle preceding vertex of order, completes the candidate degree on each vertex more
Newly.
3. the single-wheel core value maintaining method of multiple edge update under a kind of Dynamic Graph according to claim 1, which is characterized in that institute
It states and judges whether the vertex v is that core value increases point, specifically:
Judge the OkWhether the candidate degree of middle vertex v and the adduction of stop degree are greater than k, if so, judging that vertex v is that core value increases
Otherwise point judges that vertex v is that non-core value increases point.
4. the single-wheel core value maintaining method of multiple edge update under a kind of Dynamic Graph according to any one of claims 1 to 3, special
Sign is that the stop degree on each vertex is preset as zero in the current Dynamic Graph；
Then S4 includes:
S4.1, if so, in the OkThe stop degree that middle order comes neighbours vertex thereafter adds 1, and to the OkMiddle order follows top closely
Next vertex of point v executes S3；If it is not, executing S4.2；
Whether S4.2, the stop degree for judging the vertex v are zero, if so, according to order come each vertex thereafter candidate degree and
Stop degree selects next vertex to execute S3；If it is not, executing S4.3；
S4.3, the adduction that the candidate degree of vertex v is updated to current candidate degree and stop degree update the stop degree of vertex v
It is zero, transmitting the vertex v core value increased cannot influence, and candidate degree and the stop on each vertex thereafter are come according to order
Degree selects next vertex to execute S3.
5. the single-wheel core value maintaining method of multiple edge update under a kind of Dynamic Graph according to claim 4, which is characterized in that institute
It states in S4.2, the candidate degree and stop degree that each vertex thereafter is come according to order selects next vertex to execute S3, tool
Body are as follows:
Judge the OkIn come first candidate degree after vertex v with the presence or absence of order and be greater than the vertex u of k or stop degree greater than 0,
If so, vertex u is determined as next vertex and executes S3, if it is not, the then OkIn all vertex traversed.
6. the single-wheel core value maintaining method of multiple edge update under a kind of Dynamic Graph according to claim 4, which is characterized in that institute
It states in S4.3, described transmitting not increased influence of vertex v core value, specifically:
(a) the candidate degree that each of the vertex v belongs to the neighbours vertex m that core value increases point is subtracted 1, if the time of neighbours vertex m
The sum of degree of choosing and stop degree are less than k, then the core value for deleting neighbours vertex m increases the label of point, and updates neighbours vertex m's
Candidate degree is the adduction of current candidate degree and stop degree, stop degree is zero；
(b) to each neighbours vertex w of neighbours vertex m, if neighbours vertex w is in OkIn come the vertex v after, then will be adjacent
The stop degree for occupying vertex w subtracts 1, and otherwise, opposite vertexes w repeats the transmitting operation such as opposite vertexes m in step (a).
7. the single-wheel core value maintaining method of multiple edge update under a kind of Dynamic Graph, which is characterized in that when the Dynamic Graph in social networks
When lower deletion point or side, submethod is safeguarded using vertex core value when deleting point or side under Dynamic Graph, which safeguards son side
Method includes:
S1, the goodness number and core value for determining each vertex in current Dynamic Graph；
S2, based on all points to be deleted or side, update the goodness number on each vertex；
S3, the vertex that its each goodness number is less than its core value is determined as to core value reduction point；
S4, the core value that point is reduced based on each core value determine that the core value of other omissions reduces point from all vertex；
S5, the core value and goodness number for updating each core value reduction point, and S3 is repeated, until there is no core values to reduce point, obtain
To the core value updated value on each vertex, the maintenance of core value is completed.
8. the single-wheel core value maintaining method of multiple edge update under a kind of Dynamic Graph according to claim 7, which is characterized in that institute
Stating S4 includes:
Determine that each core value reduces its core value of each of point and reduces the equal neighbours vertex of the core value put with the core value, and by each neighbour
The goodness number for occupying vertex subtracts 1, if the goodness number on the neighbours vertex is less than its core value, which is determined as core value and is reduced
Point.
9. the single-wheel core value maintaining method of multiple edge update, feature exist under a kind of Dynamic Graph according to claim 7 or 8
In the S5 includes
The core value that each core value reduces point is subtracted 1 and updates goodness number, if the core value reduces point and repeats S3, otherwise, is then deleted
Except the vertex is the label that core value reduces point, until there is no core values to reduce point, the core value updated value on each vertex is obtained, is completed
The maintenance of core value.
10. a kind of storage medium, which is characterized in that instruction is stored in the storage medium, when computer reads described instruction
When, execute the computer above-mentioned such as insertion point or Bian Shiding under any Dynamic Graph as claimed in any one of claims 1 to 6
Point or side Shi Dingdian are deleted under point core value maintenance submethod and/or such as described in any item any Dynamic Graphs of claim 7 to 9
Core value safeguards submethod.
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